Question

In YDSE, find the thickness (in $\mu m$) of a glass slab $(\mu =1.5)$ which should be placed before the upper slit $S_1$ so that the central maximum now lies at a point where 5th bright fringe was lying earlier (before inserting the slab). Wavelength of light used is $5000\mathring{A}$.

Answer 1

Path difference at the point of 5th bright fringe before insertion of glass slab=$5\lambda$

Position of 5th bright fringe, y, is given by $\frac{yd}{D}=5\lambda$$

Path difference added due to insertion of glass slab = $t(\mu -1))$

The path difference between interfering beams at the point of central maximum= $0=t(\mu -1))-\frac{yd}{D}$

Hence, $t(\mu -1)=\frac{yd}{D}=5\lambda$

Therefore, $t=\frac{5\lambda }{\mu -1}=5\times {10}^{-6}m$